It has always been a huge challenge to construct high-strength hydrogels that are composed entirely of natural polymers. In this study, inspired by the structural characteristics of the extracellular matrix (ECM), gelatin and hydrazide alginate were employed to mimic the composition of collagen and glycosaminoglycans (GAGs) in the ECM, respectively, to develop natural polymer (NP) high-strength hydrogels crosslinked by physical and covalent interactions (Gelatin-HAlg-DN). First, HAlg and gelatin can form physically crosslinked hydrogels (Gelatin-HAlg) due to electrostatic and hydrogen bond interactions. Then, the Gelatin-HAlg hydrogels can be further covalently crosslinked in the presence of 1-(3-dimethylaminopropyl)-3-ethyl carbodiimide hydrochloride (EDC) and N-hydroxysuccinimide (NHS) to obtain Gelatin-HAlg-DN hydrogels. The obtained Gelatin-HAlg-DN hydrogels exhibit considerably enhanced mechanical properties (tensile strength: 0.9 MPa; elongation at break: 177%) with a maximum 16- and 3.2-fold increase in tensile strength and elongation at break, respectively, compared with gelatin methacrylate (GelMA) hydrogels. Importantly, the Gelatin-HAlg-DN hydrogels exhibit excellent biodegradability and swelling stability under physiological conditions, and the capability to support cell adhesion and proliferation. In a rat critical size bone defect model, Gelatin-HAlg-DN hydrogels loaded with psoralen could effectively promote bone regeneration, showing appealing potential as tissue engineering scaffolds.